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IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryGeometry ToolkitArcs & Sectors Using Radians

Arcs & Sectors Using Radians (DP IB Applications & Interpretation (AI)): Revision Note

Amber

Written by: Amber

Reviewed by: Dan Finlay

Updated on

DP Applications & Interpretation (AI): HLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SL

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Arcs & Sectors Using Radians

How do I use radians to find the length of an arc?

  • The formula is l equals r theta

    • l is the length of the arc

    • theta is the angle measured in radians

    • r is the radius

Radian Measure Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

How do I use radians to find the area of a sector?

  • The formula is A equals 1 half r squared theta

    • A is the area of the sector

    • theta is the angle measured in radians

    • r is the radius

Diagram showing the area of a sector with centre O, radius r, angle θ, and formula A = 1/2 r²θ. Points P and Q are on the circle's edge.

Examiner Tips and Tricks

You do not need to remember this formula, as it is in the geometry and trigonometry section of the formula booklet.

Worked Example

A slice of cake forms a sector of a circle with an angle of straight pi over 6 radians and radius of 7 cm. Find the area of the surface of the slice of cake and its perimeter.

 

aa-sl-3-1-3-arcs-and-sectors-using-radians-we-solution

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    Author
    Reviewer
    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.